This implements the accelerated failure time models S_0(t exp(beta x))
and S_0(int_0^t exp(beta x(u)) du). The baseline function S_0(t*) is
modelled as exp(-exp(eta_0(log(t*)))), where eta_0(log(t*)) is a linear
predictor using natural splines.

R implementation of generalized survival models (GSMs), smooth accelerated failure time (AFT) models and Markov multi-state models. For the GSMs, g(S(t|x))=eta(t,x) for a link function g, survival S at time t with covariates x and a linear predictor eta(t,x). The main assumption is that the time effect(s) are smooth <doi:10.1177/0962280216664760>. For fully parametric models with natural splines, this re-implements Stata's 'stpm2' function, which are flexible parametric survival models developed by Royston and colleagues. We have extended the parametric models to include any smooth parametric smoothers for time. We have also extended the model to include any smooth penalized smoothers from the 'mgcv' package, using penalized likelihood. These models include left truncation, right censoring, interval censoring, gamma frailties and normal random effects <doi:10.1002/sim.7451>, and copulas. For the smooth AFTs, S(t|x) = S_0(t*eta(t,x)), where the baseline survival function S_0(t)=exp(-exp(eta_0(t))) is modelled for natural splines for eta_0, and the time-dependent cumulative acceleration factor eta(t,x)=\int_0^t exp(eta_1(u,x)) du for log acceleration factor eta_1(u,x). The Markov multi-state models allow for a range of models with smooth transitions to predict transition probabilities, length of stay, utilities and costs, with differences, ratios and standardisation.

Mark Clements

rstpm2

Smooth Survival Models, Including Generalized Survival Models

Xing-Rong Liu

Benjamin Christoffersen

Paul Lambert

Lasse Hjort Jakobsen

Alessandro Gasparini

Gordon Smyth

Patrick Alken

Simon Wood

Rhys Ulerich

aft function

Parametric accelerated failure time model with smooth time functions — aft

<dl>

 <dt>formula</dt>
<dd>a formula object, with the response on the left of a <code>~</code> operator,
and the regression terms (excluding time) on the right. The response
should be a survival object as returned by the <code><a href='https://rdrr.io/pkg/survival/man/Surv.html'>Surv</a></code>
function. The terms can include linear effects for any time-varying
coefficients. [required]</dd>

 <dt>data</dt>
<dd>a data-frame in which to interpret the variables named in the
<code>formula</code> argument. [at present: required]</dd>

 <dt>smooth.formula</dt>
<dd>a formula for describing the time effects for the linear predictor,
excluding the baseline S_0(t*), but including time-dependent
acceleration factors. The time-dependent acceleration factors can be
modelled with any smooth functions.</dd>

 <dt>df</dt>
<dd>an integer that describes the degrees of freedom for the <code>ns</code>
function for modelling the baseline log-cumulative hazards function (default=3).</dd>

 <dt>tvc</dt>
<dd>a list with the names of the time-varying coefficients. This uses natural splines
(e.g. <code>tvc=list(hormon=3)</code> is equivalent to
<code>smooth.formula=~...+hormon:nsx(log(time),df=3)</code>), which by default
does not include an intercept (or main effect) term.</dd>

 <dt>cure.formula</dt>
<dd>a formula for describing the cure fraction.</dd>

 <dt>control</dt>
<dd><code>control</code> argument passed to <code>optim</code>.</dd>

 <dt>init</dt>
<dd><code>init</code> should either be <code>FALSE</code>, such that initial
 values will be determined using Cox regression, or a numeric
 vector of initial values.</dd>

<dt>weights</dt>
<dd>an optional vector of 'prior weights' to be used in the
 fitting process. Should be <code>NULL</code> or a numeric vector.</dd>

 <dt>tvc.intercept</dt>
<dd>logical for whether to include an intercept in the time-varying
acceleration factor (defaults to TRUE)</dd>

 <dt>tvc.integrated</dt>
<dd>logical for whether the time-varying
acceleration factor should be based on a integration, rather than a
cumulative effect (defaults to FALSE)</dd>

 <dt>timeVar</dt>
<dd>string variable defining the time variable. By default, this is
determined from the survival object, however this may be ambiguous if
two variables define the time.</dd>

<dt>time0Var</dt>
<dd>string variable to determine the entry variable; useful
 for when more than one data variable is used in the entry time.</dd>

 <dt>cure</dt>
<dd>logical for whether to model for cure using a non-mixture model (default=FALSE)</dd>

 <dt>mixture</dt>
<dd>logical for whether to model for cure using a mixture model (default=FALSE)</dd>

 <dt>contrasts</dt>
<dd>an optional list. See the <code>contrasts.arg</code>
 of <code><a href='https://rdrr.io/r/stats/model.matrix.html'>model.matrix.default</a></code>.</dd>

 <dt>subset</dt>
<dd>an optional vector specifying a subset of observations to
 be used in the fitting process.</dd>

 <dt>...</dt>
<dd>additional arguments to be passed to the <code>mle2</code>.</dd>

</dl>

Arguments

Author

Parametric accelerated failure time model with smooth time functions

aft: Parametric accelerated failure time model with smooth time functions

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Examples